Graph (x^2)/25+(y^2)/64=1

Problem

(x2)/25+(y2)/64=1

Solution

1. Identify the type of conic section. Since the equation is in the form (x2)/(a2)+(y2)/(b2)=1 with positive coefficients, it is an ellipse centered at the origin (0,0)

2. Determine the values of a and b by taking the square roots of the denominators. Here, a2=25 so a=5 and b2=64 so b=8

3. Locate the vertices. Since b>a the major axis is vertical. The vertices are at (0,±8) and the co-vertices are at (±5,0)

4. Calculate the foci using the formula c2=|a2−b2| Here, c2=|25−64|=39 so c=√(,39)≈6.24 The foci are located at (0,±√(,39))

5. Sketch the graph by plotting the center (0,0) the vertices (0,8) and (0,−8) and the co-vertices (5,0) and (−5,0) then drawing a smooth curve through these points.

Final Answer

(x2)/25+(y2)/64=1* is an ellipse with vertices at *(0,±8)* and co-vertices at *(±5,0)

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